World Scientific Lecture Notes in Physics - Vol. 46
SYMMETRIES AND CURVATURE STRUCTURE IN GENERAL RELATIVITY
by G S Hall (University of Aberdeen, UK)
This is a text on classical general relativity from a geometrical viewpoint. Introductory chapters are provided on algebra, topology and manifold theory, together with a chapter on the basic ideas of space-time manifolds and Einstein's theory. There is a detailed account of algebraic structures and tensor classification in general relativity and also of the relationships between the metric, connection and curvature structures on space-times. The latter includes chapters on holonomy and sectional curvature. An extensive study is presented of symmetries in general relativity, including isometries, homotheties, conformal symmetries and affine, projective and curvature collineations. Several general properties of such symmetries are studied and a preparatory section on transformation groups and on the properties of Lie algebras of vector fields on manifolds is provided.
Contents:
- Introduction
- Algebraic Concepts
- Topology
- Manifold Theory
- Lie
Groups
- The Lorentz Group
- Space-Times and Algebraic Classification
- Holonomy Groups and General Relativity
- The Connection and Curvature Structure of Space-Time
- Affine Vector Fields on Space-Time
- Conformal Symmetry in Space-Times
- Projective Symmetry in Space-Times
- Curvature Collineations
Readership: Graduate students, lecturers and researchers in mathematical and
theoretical physics.
“This book is strongly recommended to everyone who wants to get a mathematically rigorous as well as readable presentation of the underlying pseudo-Riemannian manifolds of General Relativity Theory.”
“... it is a complete and thorough review of the subject from a consistent point of view. It covers some most important mathematical aspects of Einstein's theory of general relativity. Written by a leading authority on the topic, this monograph is sure to become a standard reference in this field.”
“The book is a thorough and in depth exposition of its subject written in a consistent way ... This will make it a pleasant read not only for students and researchers in physics but also in mathematics. It is a safe bet that this monograph soon will become a standard reference in the field.”
| Monatshefte für Mathematik |
"Overall this book presents a wealth of results on the geometry of four-dimensional space-times in a well organized and carefully presented form. Most of them are perhaps rather technical or specialized but they will certainly be useful, in particular, for workers on exact solutions of Einstein's equations."
| General Relativity and Gravitation |
| 440pp |
Pub. date: Apr 2004 |
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